Eigenvalue Problems for Exponential-Type Kernels
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-JRNL-755085. The second author was partially supported by NSF under grant DMS-1619640.
Computational Methods in Applied Mathematics
We study approximations of eigenvalue problems for integral operators associated with kernel functions of exponential type. We show convergence rate |λk − λk,h| ≤ Ckh 2 in the case of lowest order approximation for both Galerkin and Nyström methods, where h is the mesh size, λk and λk,h are the exact and approximate kth largest eigenvalues, respectively. We prove that the two methods are numerically equivalent in the sense that |λk,h(G)-λk,h(N)| ≤ Ch2, where λk,h(G) and λk,h(N) denote the kth largest eigenvalues computed by Galerkin and Nyström methods, respectively, and C is a eigenvalue independent constant. The theoretical results are accompanied by a series of numerical experiments
Locate the Document
Cai, D., & Vassilevski, P. S. (2020). Eigenvalue Problems for Exponential-Type Kernels. Computational Methods in Applied Mathematics, 20(1), 61-78.